Bernstein, Birkner, Lange and Peters present GMP-EECM, a variant of GMP-ECM (and developed from it) but using Edwards curves, rather than the more standard Montgomery curves of regular GMP-ECM.
http://cr.yp.to/papers.html#eecm
In one of their tests, this reduced the stage 1 time from 2448mS to 2276mS.
Alex Kruppa has stated that this improvement will also be incorporated into some future version of GMP-ECM.
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